In
mathematics, a protorus is a
compact
Compact as used in politics may refer broadly to a pact or treaty; in more specific cases it may refer to:
* Interstate compact
* Blood compact, an ancient ritual of the Philippines
* Compact government, a type of colonial rule utilized in British ...
connected
Connected may refer to:
Film and television
* ''Connected'' (2008 film), a Hong Kong remake of the American movie ''Cellular''
* '' Connected: An Autoblogography About Love, Death & Technology'', a 2011 documentary film
* ''Connected'' (2015 TV ...
topological abelian group
In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing h ...
. Equivalently, it is a
projective limit
In mathematics, the inverse limit (also called the projective limit) is a construction that allows one to "glue together" several related objects, the precise gluing process being specified by morphisms between the objects. Thus, inverse limits c ...
of
tori (products of a finite number of copies of the
circle group), or the
Pontryagin dual
In mathematics, Pontryagin duality is a duality between locally compact abelian groups that allows generalizing Fourier transform to all such groups, which include the circle group (the multiplicative group of complex numbers of modulus one), ...
of a discrete torsion-free
abelian group
In mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written. That is, the group operation is comm ...
.
Some examples of protori are given by
solenoid groups.
See also
*
Duocylinder
The duocylinder, also called the double cylinder or the bidisc, is a geometric object embedded in 4- dimensional Euclidean space, defined as the Cartesian product of two disks of respective radii ''r''1 and ''r''2:
:D = \left\
It is analogo ...
-
Cartesian product of two
disks
*
Proprism
In geometry of 4 dimensions or higher, a proprism is a polytope resulting from the Cartesian product of two or more polytopes, each of two dimensions or higher. The term was coined by John Horton Conway for ''product prism''. The dimension of the ...
References
*
Topological groups
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